The Classic Controller for the Wii is designed for those who want a more traditional, relaxed experience when playing their games. As fun as motion control with the Wiimote may be, sometimes you just want to slouch back in your chair and lazily play with a regular controller.
The classic controller's button layout is much like the PS2's DualShock. It features a D-Pad on the left, dual analogs at the bottom, and four face buttons on the right along with shoulder buttons on the back.
The controller really comes in handy for virtual console games, which don't always go well with the default Wii control scheme. Some of them won't even load unless a classic controller is detected.
The Classic Controller will also play a large part in the upcoming Super Smash Bros Brawl and I fully reccomend it.